Stable Parametric Programming:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
2001
|
| Schriftenreihe: | Applied Optimization
57 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nonlinear programming. Then new results in convex programming, using LFS functions, for single-objective, multi-objective, differentiable and non-smooth programs are introduced. Parametric programming models are studied using basic tools of point-to-set topology. Stability of the models is introduced, essentially, as continuity of the feasible set of decision variables under continuous perturbations of the parameters. Perturbations that preserve this continuity are regions of stability. It is shown how these regions can be identified. The main results on stability are characterizations of locally and globally optimal parameters for stable and also for unstable perturbations. The results are straightened for linear models and bi-level programs. Some of the results are extended to abstract spaces after considering parameters as 'controls'. Illustrations from diverse fields, such as data envelopment analysis, management, von Stackelberg games of market economy, and navigation problems are given and several case studies are solved by finding optimal parameters. The book has been written in an analytic spirit. Many results appear here for the first time in book form. Audience: The book is written at the level of a first-year graduate course in optimization for students with varied backgrounds interested in modeling of real-life problems. It is expected that the reader has been exposed to a prior elementary course in optimization, such as linear or non-linear programming. The last section of the book requires some knowledge of functional analysis |
| Beschreibung: | 1 Online-Ressource (XXII, 322 p) |
| ISBN: | 9781461500117 9781461348856 |
| ISSN: | 1384-6485 |
| DOI: | 10.1007/978-1-4615-0011-7 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042420837 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2001 |||| o||u| ||||||eng d | ||
| 020 | |a 9781461500117 |c Online |9 978-1-4615-0011-7 | ||
| 020 | |a 9781461348856 |c Print |9 978-1-4613-4885-6 | ||
| 024 | 7 | |a 10.1007/978-1-4615-0011-7 |2 doi | |
| 035 | |a (OCoLC)863912181 | ||
| 035 | |a (DE-599)BVBBV042420837 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 519.6 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Zlobec, Sanjo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stable Parametric Programming |c by Sanjo Zlobec |
| 264 | 1 | |a Boston, MA |b Springer US |c 2001 | |
| 300 | |a 1 Online-Ressource (XXII, 322 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Applied Optimization |v 57 |x 1384-6485 | |
| 500 | |a Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nonlinear programming. Then new results in convex programming, using LFS functions, for single-objective, multi-objective, differentiable and non-smooth programs are introduced. Parametric programming models are studied using basic tools of point-to-set topology. Stability of the models is introduced, essentially, as continuity of the feasible set of decision variables under continuous perturbations of the parameters. Perturbations that preserve this continuity are regions of stability. It is shown how these regions can be identified. The main results on stability are characterizations of locally and globally optimal parameters for stable and also for unstable perturbations. The results are straightened for linear models and bi-level programs. Some of the results are extended to abstract spaces after considering parameters as 'controls'. Illustrations from diverse fields, such as data envelopment analysis, management, von Stackelberg games of market economy, and navigation problems are given and several case studies are solved by finding optimal parameters. The book has been written in an analytic spirit. Many results appear here for the first time in book form. Audience: The book is written at the level of a first-year graduate course in optimization for students with varied backgrounds interested in modeling of real-life problems. It is expected that the reader has been exposed to a prior elementary course in optimization, such as linear or non-linear programming. The last section of the book requires some knowledge of functional analysis | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Computer engineering | |
| 650 | 4 | |a Economics | |
| 650 | 4 | |a Operations research | |
| 650 | 4 | |a Operations Research, Management Science | |
| 650 | 4 | |a Operation Research/Decision Theory | |
| 650 | 4 | |a Optimization | |
| 650 | 4 | |a Economic Theory | |
| 650 | 4 | |a Electrical Engineering | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Wirtschaft | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4615-0011-7 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027856254 | ||
Datensatz im Suchindex
| _version_ | 1804153093238030336 |
|---|---|
| any_adam_object | |
| author | Zlobec, Sanjo |
| author_facet | Zlobec, Sanjo |
| author_role | aut |
| author_sort | Zlobec, Sanjo |
| author_variant | s z sz |
| building | Verbundindex |
| bvnumber | BV042420837 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863912181 (DE-599)BVBBV042420837 |
| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4615-0011-7 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03372nmm a2200505zcb4500</leader><controlfield tag="001">BV042420837</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2001 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461500117</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4615-0011-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461348856</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4613-4885-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4615-0011-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863912181</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042420837</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.6</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Zlobec, Sanjo</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Stable Parametric Programming</subfield><subfield code="c">by Sanjo Zlobec</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston, MA</subfield><subfield code="b">Springer US</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XXII, 322 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Applied Optimization</subfield><subfield code="v">57</subfield><subfield code="x">1384-6485</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nonlinear programming. Then new results in convex programming, using LFS functions, for single-objective, multi-objective, differentiable and non-smooth programs are introduced. Parametric programming models are studied using basic tools of point-to-set topology. Stability of the models is introduced, essentially, as continuity of the feasible set of decision variables under continuous perturbations of the parameters. Perturbations that preserve this continuity are regions of stability. It is shown how these regions can be identified. The main results on stability are characterizations of locally and globally optimal parameters for stable and also for unstable perturbations. The results are straightened for linear models and bi-level programs. Some of the results are extended to abstract spaces after considering parameters as 'controls'. Illustrations from diverse fields, such as data envelopment analysis, management, von Stackelberg games of market economy, and navigation problems are given and several case studies are solved by finding optimal parameters. The book has been written in an analytic spirit. Many results appear here for the first time in book form. Audience: The book is written at the level of a first-year graduate course in optimization for students with varied backgrounds interested in modeling of real-life problems. It is expected that the reader has been exposed to a prior elementary course in optimization, such as linear or non-linear programming. The last section of the book requires some knowledge of functional analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer engineering</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Economics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operations research</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operations Research, Management Science</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operation Research/Decision Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Economic Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Electrical Engineering</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Wirtschaft</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4615-0011-7</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027856254</subfield></datafield></record></collection> |
| id | DE-604.BV042420837 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461500117 9781461348856 |
| issn | 1384-6485 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856254 |
| oclc_num | 863912181 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XXII, 322 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer US |
| record_format | marc |
| series2 | Applied Optimization |
| spelling | Zlobec, Sanjo Verfasser aut Stable Parametric Programming by Sanjo Zlobec Boston, MA Springer US 2001 1 Online-Ressource (XXII, 322 p) txt rdacontent c rdamedia cr rdacarrier Applied Optimization 57 1384-6485 Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nonlinear programming. Then new results in convex programming, using LFS functions, for single-objective, multi-objective, differentiable and non-smooth programs are introduced. Parametric programming models are studied using basic tools of point-to-set topology. Stability of the models is introduced, essentially, as continuity of the feasible set of decision variables under continuous perturbations of the parameters. Perturbations that preserve this continuity are regions of stability. It is shown how these regions can be identified. The main results on stability are characterizations of locally and globally optimal parameters for stable and also for unstable perturbations. The results are straightened for linear models and bi-level programs. Some of the results are extended to abstract spaces after considering parameters as 'controls'. Illustrations from diverse fields, such as data envelopment analysis, management, von Stackelberg games of market economy, and navigation problems are given and several case studies are solved by finding optimal parameters. The book has been written in an analytic spirit. Many results appear here for the first time in book form. Audience: The book is written at the level of a first-year graduate course in optimization for students with varied backgrounds interested in modeling of real-life problems. It is expected that the reader has been exposed to a prior elementary course in optimization, such as linear or non-linear programming. The last section of the book requires some knowledge of functional analysis Mathematics Mathematical optimization Computer engineering Economics Operations research Operations Research, Management Science Operation Research/Decision Theory Optimization Economic Theory Electrical Engineering Mathematik Wirtschaft https://doi.org/10.1007/978-1-4615-0011-7 Verlag Volltext |
| spellingShingle | Zlobec, Sanjo Stable Parametric Programming Mathematics Mathematical optimization Computer engineering Economics Operations research Operations Research, Management Science Operation Research/Decision Theory Optimization Economic Theory Electrical Engineering Mathematik Wirtschaft |
| title | Stable Parametric Programming |
| title_auth | Stable Parametric Programming |
| title_exact_search | Stable Parametric Programming |
| title_full | Stable Parametric Programming by Sanjo Zlobec |
| title_fullStr | Stable Parametric Programming by Sanjo Zlobec |
| title_full_unstemmed | Stable Parametric Programming by Sanjo Zlobec |
| title_short | Stable Parametric Programming |
| title_sort | stable parametric programming |
| topic | Mathematics Mathematical optimization Computer engineering Economics Operations research Operations Research, Management Science Operation Research/Decision Theory Optimization Economic Theory Electrical Engineering Mathematik Wirtschaft |
| topic_facet | Mathematics Mathematical optimization Computer engineering Economics Operations research Operations Research, Management Science Operation Research/Decision Theory Optimization Economic Theory Electrical Engineering Mathematik Wirtschaft |
| url | https://doi.org/10.1007/978-1-4615-0011-7 |
| work_keys_str_mv | AT zlobecsanjo stableparametricprogramming |